{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-parallel-projection-method-for-metric","title":"A Parallel Projection Method for Metric Constrained Optimization","arxiv_id":"1901.10084","date":"2019-01-29","proceeding":null,"authors":["Cameron Ruggles","Nate Veldt","David F. Gleich"],"abstract":"Many clustering applications in machine learning and data mining rely on\nsolving metric-constrained optimization problems. These problems are\ncharacterized by $O(n^3)$ constraints that enforce triangle inequalities on\ndistance variables associated with $n$ objects in a large dataset. Despite its\nusefulness, metric-constrained optimization is challenging in practice due to\nthe cubic number of constraints and the high-memory requirements of standard\noptimization software. Recent work has shown that iterative projection methods\nare able to solve metric-constrained optimization problems on a much larger\nscale than was previously possible, thanks to their comparatively low memory\nrequirement. However, the major limitation of projection methods is their slow\nconvergence rate. In this paper we present a parallel projection method for\nmetric-constrained optimization which allows us to speed up the convergence\nrate in practice. The key to our approach is a new parallel execution schedule\nthat allows us to perform projections at multiple metric constraints\nsimultaneously without any conflicts or locking of variables. We illustrate the\neffectiveness of this execution schedule by implementing and testing a parallel\nprojection method for solving the metric-constrained linear programming\nrelaxation of correlation clustering. We show numerous experimental results on\nproblems involving up to 2.9 trillion constraints.","url_abs":"http://arxiv.org/abs/1901.10084v1","url_pdf":"http://arxiv.org/pdf/1901.10084v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-parallel-projection-method-for-metric","repo_url":"https://github.com/camruggles/ParallelDykstras","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1901.10084","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}